   Chapter 5.5, Problem 46E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Evaluate the indefinite integral. ∫ x 2 2 + x   d x

To determine

To evaluate: The indefinite integral.

Explanation

Given:

The indefinite integral function is x22+xdx.

Calculation:

Take the consideration as follows:

u=2+xx=u2

Differentiate both sides of the equation.

dx=du

The indefinite integral function is,

x22+xdx (1)

Substitute x for (u2), u for (2+x), and du for dx in Equation (1).

x22+xdx=(u2)2udu=(u24u+4)u12du=(u2+124u1+12+4u12)du=(u524u32+4u12)du

=u52du4u32du+4u12du=u52du4u32du+4u12du (2)

Integrate Equation (2)

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 